Basically, the idea is that by using the above two, you can reduce the number of unknown variables.

Let's take a simpler example:

$\displaystyle 2x + y = -3$
$\displaystyle x + 3y = 5$

So, we have two unknown variables and two unique equations. That means we have enough information to find a solution.

Let's try both methods:

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1. By elimination:

We can choose whether to eliminate the x or the y first. Let's eliminate the x.

In order to eliminate x, we need to make the x-terms on both equations the same magnitude. At the moment, we have an x and a 2x, so they are not the same. We can make them the same by multiplying or dividing one of the equations. In our case, we want to multiply both sides of the second equation by 2 so that the x becomes a 2x. So

$\displaystyle x + 3y = 5$

becomes

$\displaystyle 2x + 6y = 10$

Now we are working with

2x + y = -3
2x + 6y = 10

So far so good. Now let's subtract the first equation from the second. We do this term by term:

These techniques can apply for any set of simultaneous equations, no matter how complicated those equations are or how many you have in your set of simultaneous equations. However, as the problems get more difficult, you will need to rely more on substitution than elimination. You should practice both because both methods are very useful

I don't think there should be a lot of problem. Start with the third equation as that is expressed in terms of two variables only then put the value of y or z obtained from their to the first two equations, this will leave you with two equations with two variables and in this way you may solve it. I am not solving it here because i believe practice makes a man perfect and a true mathematics lover will just guide you the path and leave you alone to walk on it.